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M. Baake, A.C.D. van Enter
Close-packed dimers on the line: Diffraction versus dynamical spectrum
(52K, latex)
ABSTRACT. Abstract. The translation action of R^d on a translation bounded measure leads to an interesting class of dynamical systems, with a rather rich spectral theory. In general, the diffraction spectrum of , which is the carrier of the diffraction measure, lives on a subset
of the dynamical spectrum. It is known that, under some mild assumptions, a pure point diffraction spectrum implies a pure point dynamical spectrum (the opposite implication always being true). For other systems, the diffraction spectrum can be a proper subset of
the dynamical spectrum, as was pointed out for the Thue-Morse sequence (with singular continuous diffraction) in [17]. Here, we construct a random system of close-packed dimers on the line that have some underlying long-range periodic order as well, and display the same
type of phenomenon for a system with absolutely continuous spectrum. An interpretation in terms of atomic versus molecular spectrum suggests a way to come to a more general
correspondence between these two types of spectra.